Multi-pair transceiver decoder system with low computation slicer

ABSTRACT

A method and a system for decoding information signals encoded by a multi-state encoding architecture and transmitted over a multi-dimensional transmission channel by computing a distance of a received word from a codeword. One-dimensional (1D) input signals are detected in a symbol decoder, implemented using look-up tables, to produce a pair of 1D errors, with each representing a distance metric between the input signal and a symbol in one of two disjoint symbol-subsets. The symbol decoder is implemented as a pair of slicers, each detecting an input signal with respect to one of two disjoint symbol-subsets. A third slicer detects the input with respect to the union of the two disjoint symbol-subsets. Decisions from the first, second and third slicers are processed to define 1D square error terms expressed in Hamming metrics. Reduced bit count error terms allow follow-on error processing to be performed with a minimum of computational complexity. The 1D errors are combined to produce a set of multi-dimensional error terms. Each of the multi-dimensional error terms corresponds to a distance between a received word and a nearest codeword.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of Application Ser. No.09/370,353, filed Aug. 9, 1999, U.S. Pat. No. 6,226,332, which claimspriority on the basis of the following provisional applications: Ser.No. 60/130,616 entitled “Multi-Pair Gigabit Ethernet Transceiver” filedon Apr. 22, 1999, Ser. No. 60/116,946 entitled “Multiple DecisionFeedback Equalizer” filed on Jan. 20, 1999, and Ser. No. 60/108,319entitled “Gigabit Ethernet Transceiver” filed on Nov. 13, 1998.

The present application is related to the applications filed on Aug. 9,1999 and assigned to the same assignee, the contents of each of whichare herein incorporated by reference as follows: Ser. No. 09/370,491entitled “High-Speed Decoder for a Multi-Pair Gigabit Transceiver,” Ser.No. 09/370,370 entitled “System and Method for Trellis Decoding in aMulti-Pair Transceiver System,” Ser. No. 09/370,354 entitled “System andMethod for High Speed Decoding and ISI Compensation in a Multi-PairTransceiver System.”

FIELD OF THE INVENTION

The present invention relates generally to methods and systems fordecoding signals encoded with a multi-state encoding architecture in ahigh-speed communication system and, more particularly, the inventionrelates to a method and a system for decoding the trellis code specifiedin the IEEE 802.3ab standard for Gigabit Ethernet (1000BASE-T) with aminimum of computational complexity and propagation delays in the logiccircuits.

DESCRIPTION OF THE RELATED ART

In recent years, local area network (LAN) applications have become moreand more prevalent as a means for providing local interconnect betweenpersonal computer systems, work stations and servers. Because of thebreadth of its installed base, the 10BASE-T implementation of Ethernetremains the most pervasive if not the dominant, network technology forLANs. However, as the need to exchange information becomes more and moreimperative, and as the scope and size of the information being exchangedincreases, higher and higher speeds (greater bandwidth) are requiredfrom network interconnect technologies. Among the highspeed LANtechnologies currently available, fast Ethernet, commonly termed100BASE-T, has emerged as the clear technological choice. Fast Ethernettechnology provides a smooth, non-disruptive evolution from the 10megabit per second (Mbps) performance of 10BASE-T applications to the100 Mbps performance of 100BASE-T. The growing use of 100BASE-Tinterconnections between servers and desktops is creating a definiteneed for an even higher speed network technology at the backbone andserver level.

One of the more suitable solutions to this need has been proposed in theIEEE 802.3ab standard for gigabit ethernet, also termed 1000BASE-T.Gigabit ethernet is defined as able to provide 1 gigabit per second(Gbps) bandwidth in combination with the simplicity of an ethernetarchitecture, at a lower cost than other technologies of comparablespeed. Moreover, gigabit ethernet offers a smooth, seamless upgrade pathfor present 10BASE-T or 100BASE-T ethernet installations.

In order to obtain the requisite gigabit performance levels, gigabitethernet transceivers are interconnected with a multi-pair transmissionchannel architecture. In particular, transceivers are interconnectedusing four separate pairs of twisted Category-5 copper wires. Gigabitcommunication, in practice, involves the simultaneous, paralleltransmission of information signals, with each signal conveyinginformation at a rate of 250 megabits per second (Mb/s). Simultaneous,parallel transmission of four information signals over four twisted wirepairs poses substantial challenges to bidirectional communicationtransceivers, even though the data rate on any one wire pair is “only”250 Mbps.

In particular, the gigabit ethernet standard requires that digitalinformation being processed for transmission be symbolically representedin accordance with a five-level pulse amplitude modulation scheme(PAM-5) and encoded in accordance with an 8-state Trellis codingmethodology. Coded information is then communicated over amulti-dimensional parallel transmission channel to a designatedreceiver, where the original information must be extracted (demodulated)from a multi-level signal. In gigabit Ethernet, it is important to notethat it is the concatenation of signal samples received simultaneouslyon all four twisted pair lines of the channel that defines a symbol.Thus, demodulator/decoder architectures must be implemented with adegree of computational complexity that allows them to accommodate notonly the “state width” of Trellis coded signals, but also the“dimensional depth” represented by the transmission channel.

Computational complexity is not the only challenge presented to moderngigabit capable communication devices. A perhaps greater challenge isthat the complex computations required to process “deep” and “wide”signal representations must be performed in an almost vanishingly smallperiod of time. For example, in gigabit applications, each of thefour-dimensional signal samples, formed by the four signals receivedsimultaneously over the four twisted wire pairs, must be efficientlydecoded within a particular allocated symbol time window of about 8nanoseconds.

Successfully accomplishing the multitude of sequential processingoperations required to decode gigabit signal samples within an 8nanosecond window requires that the switching capabilities of theintegrated circuit technology from which the transceiver is constructedbe pushed to almost its fundamental limits. If performed in conventionalfashion, sequential signal processing operations necessary for signaldecoding and demodulation would result in a propagation delay throughthe logic circuits that would exceed the clock period, rendering thetransceiver circuit non-functional. Fundamentally, then, the challengeimposed by timing constraints must be addressed if gigabit Ethernet isto retain its viability and achieve the same reputation for accurate androbust operation enjoyed by its 10BASE-T and 100BASE-T siblings.

In addition to the challenges imposed by decoding and demodulatingmultilevel signal samples, transceiver systems must also be able to dealwith intersymbol interference (ISI) introduced by transmission channelartifacts as well as by modulation and pulse shaping components in thetransmission path of a remote transceiver system. During thedemodulation and decoding process of Trellis coded information, ISIcomponents are introduced by either means must also be considered andcompensated, further expanding the computational complexity and thus,system latency of the transceiver system. Without a transceiver systemcapable of efficient, high-speed signal decoding as well as simultaneousISI compensation, gigabit ethernet would likely not remain a viableconcept.

SUMMARY OF THE INVENTION

The present invention is directed to a system and method for decodinginformation coded in accordance with a multi-level encoding scheme bycomputing a distance between a received word from a codeword. Codewordsare formed from a concatenation of symbols from a multi-level symbolalphabet, with the symbols selected from two disjoint one-dimensionalsymbol subsets X and Y. A received word is represented by L inputs, withL representing the number of dimensions of a multi-dimensionalcommunication channel. Each of the L inputs uniquely corresponds to oneof the L dimensions.

A set of 1-dimensional (1D) errors is produced from the L inputs, witheach of the 1-dimensional errors representing a distance metric betweena respective one of the L inputs and a symbol in one of the two disjointone-dimensional symbol subsets. 1-dimensional errors are combined inorder to produce a set of L-dimensional errors such that each of theL-dimensional errors represents a distance between the received word anda nearest codeword among an ordered plurality of codewords.

In one aspect of the invention, each of the L inputs is sliced withrespect to each of the two disjoint symbol subsets X and Y in order toproduce a set of X-based errors, a set of Y-based errors andcorresponding sets of X-based and Y-based decisions. The sets of X-basedand Y-based errors form the set of 1-dimensional errors, while the setsof X-based and Y-based decisions forming a set of 1-dimensionaldecisions. Each of the X-based and Y-based decisions corresponds to asymbol, in a corresponding symbol subset, closest in distance (value) toone of the L inputs. Each of the 1-dimensional errors represents adistance metric between a corresponding 1-dimensional decision and therespective one of the L inputs.

In an additional aspect of the invention, each of the L inputs is slicedwith respect to each of the two disjoint symbol subsets X and Y in orderto produce a set of 1-dimensional decisions. Each of the L inputs isfurther sliced with respect to a symbol-set including all of the symbolsof the two disjoint symbol subsets in order to produce a set of harddecisions. The X-based and Y-based 1-dimensional decisions are combinedwith a set of hard decisions in order to produce a set of 1-dimensionalerrors, with each of the 1-dimensional errors representing a distancemetric between a corresponding 1-dimensional decision and a respectiveone of the L inputs. The slicers and the combination circuitry whichproduces the 1-dimensional error terms are implemented as an integratedcircuit look-up table. Combination operations and error term definitionare performed by consulting an appropriate entry in a table of entries.Error terms so developed are expressed in digital representation havingone bit.

In another aspect of the present invention, 1-dimensional errors arecombined in a first set of adders in order to produce a set of2-dimensional errors. A second set of adders combines the 2-dimensionalerrors in order to produce intermediate L-dimensional errors, with theintermediate L-dimensional errors being arranged into pairs of errorssuch that the pairs of errors correspond one-to-one to the contents ofan ordered plurality of codewords. A minimum-select module determines aminimum for each of the pairs of errors. Once determined, the minima aredefined as the L-dimensional errors.

In a particular aspect of the invention, the decoding system and methodis implemented in a bidirectional communication system in whichtransceivers are coupled together over a four twisted wire pairtransmission channel. Each of the wire pairs corresponds to an inputsuch that L equals four. Signals transmitted and received over the fourtwisted wire pair transmission channel are encoded in accordance with amulti-state trellis encoding architecture.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects and advantages of the presentinvention will be more fully understood when considered with respect tothe following detailed description, appended claims and accompanyingdrawings, wherein:

FIG. 1 is a simplified, semi-schematic block diagram of a high-speedbidirectional communication system exemplified by two transceiversconfigured to communicate over multiple twisted-pair wiring channels.

FIG. 2 is a simplified, semi-schematic block diagram of a bidirectionalcommunication transceiver system, constructed in accordance with thepresent invention.

FIG. 3 is a simplified, semi-schematic block diagram of an exemplarytrellis encoder.

FIG. 4A illustrates an exemplary PAM-5 constellation and theone-dimensional symbol-subset partitioning.

FIG. 4B illustrates the eight 4D code-subsets constructed from theone-dimensional symbol-subset partitioning of the constellation of FIG.4A.

FIG. 5 illustrates the trellis diagram for the code.

FIG. 6 is a simplified, semi-schematic block diagram of an exemplarytrellis decoder, including a Viterbi decoder, in accordance with theinvention, suitable for decoding signals coded by the exemplary trellisencoder of FIG. 3.

FIG. 7 is a simplified block diagram of a first exemplary embodiment ofa structural analog of a 1D slicing function as might be implemented inthe Viterbi decoder of FIG. 6.

FIG. 8 is a simplified block diagram of a second exemplary embodiment ofa structural analog of a 1D slicing function as might be implemented inthe Viterbi decoder of FIG. 6.

FIG. 9 is a simplified block diagram of a 2D error term generationmachine, illustrating the generation of 2D square error terms from the1D square error terms developed by the exemplary slicers of FIGS. 7 or8.

FIG. 10 is a simplified block diagram of a 4D error term generationmachine, illustrating the generation of 4D square error terms and thegeneration of extended path metrics for the 4 extended paths outgoingfrom state 0.

FIG. 11 is a simplified block diagram of a 4D symbol generation machine.

FIG. 12 illustrates the selection of the best path incoming to state 0.

FIG. 13 is a semi-schematic block diagram illustrating the internalarrangement of a portion of the path memory module of FIG. 6.

FIG. 14 is a block diagram illustrating the computation of the finaldecision and the tentative decisions in the path memory module based onthe 4D symbols stored in the path memory for each state.

FIG. 15 is a detailed diagram illustrating the processing of the outputsV₀ ^((i)), V₁ ^((i)), with i=0, . . . ,7, and V_(0F), V_(1F), V_(2F) ofthe path memory module of FIG. 6.

FIG. 16 shows the word lengths used in one embodiment of this invention.

FIG. 17 shows an exemplary lookup table suitable for use in computingsquared one-dimensional error terms.

FIGS. 18A and 18B are an exemplary look-up table which describes thecomputation of the decisions and squared errors for both the X and Ysubsets directly from one component of the 4D Viterbi input of the 1Dslicers of FIG. 7.

DETAILED DESCRIPTION OF THE INVENTION

In the context of an exemplary integrated circuit-type bidirectionalcommunication system, the present invention might be characterized as asystem and method for accommodating efficient, high speed decoding ofsignal samples encoded according to the trellis code specified in theIEEE 802.3ab standard (also termed 1000BASE-T standard).

As will be understood by one having skill in the art, high speed datatransmission is often limited by the ability of decoder systems toquickly, accurately and effectively process a transmitted symbol withina given time period. In a 1000BASE-T application (aptly termed gigabit)for example, the symbol decode period is typically taken to beapproximately 8 nanoseconds. Pertinent to any discussion of symboldecoding is the realization that 1000BASE-T systems are layered toreceive 4-dimensional (4D) signals (each signal corresponding to arespective one of four twisted pair cables) with each of the4-dimensional signals represented by five analog levels. Accordingly,the decoder circuitry portions of transceiver demodulation blocksrequire a multiplicity of operational steps to be taken in order toeffectively decode each symbol. Such a multiplicity of operations iscomputationally complex and often pushes the switching speeds ofintegrated circuit transistors which make up the computational blocks totheir fundamental limits.

In accordance with the present invention, a transceiver decoder is ableto substantially reduce the computational complexity of symbol decoding,and thus avoid substantial amounts of propagation delay (i.e., increaseoperational speed), by making use of truncated (or partial)representations of various quantities that make up the decoding/ISIcompensation process.

Sample slicing is performed in a manner such that one-dimensional (1D)square error terms are developed in a representation having, at most,three bits if the terms signify a Euclidian distance, and one bit if theterms signify a Hamming distance. Truncated 1D error term representationsignificantly reduces subsequent error processing complexity because ofthe fewer number of bits.

Likewise, ISI compensation of sample signals, prior to Viterbi decoding,is performed in a DFE, operatively responsive to tentative decisionsmade by the Viterbi. Use of tentative decisions, instead of a Viterbi'sfinal decision, reduces system latency by a factor directly related tothe path memory sequence distance between the tentative decision used,and the final decision, i.e., if there are N steps in the path memoryfrom input to final decision output, and latency is a function of N,forcing the DFE with a tentative decision at step N-6 causes latency tobecome a function of N-6. A trade-off between latency reduction andaccuracy may be made by choosing a tentative decision step either closerto the final decision point or closer to the initial point.

Computations associated with removing impairments due to intersymbolinterference (ISI) are substantially simplified, in accordance with thepresent invention, by a combination of techniques that involves therecognition that intersymbol interference results from two primarycauses, a partial response pulse shaping filter in a transmitter andfrom the characteristics of a unshielded twisted pair transmissionchannel. During the initial start-up, ISI impairments are processed inindependent portions of electronic circuitry, with ISI caused by apartial response pulse shaping filter being compensated in an inversepartial response filter in a feedforward equalizer (FFE) at systemstartup, and ISI caused by transmission channel characteristicscompensated by a decision feedback equalizer (DFE) operating inconjunction with a multiple decision feedback equalizer (MDFE) stage toprovide ISI pre-compensated signals (representing a symbol) to a decoderstage for symbolic decode. Performing the computations necessary for ISIcancellation in a bifurcated manner allows for fast DFE convergence aswell as assists a transceiver in achieving fast acquisition in a robustand reliable manner. After the start-up, all ISI is compensated by thecombination of the DFE and MDFE.

In order to appreciate the advantages of the present invention, it willbe beneficial to describe the invention in the context of an exemplarybidirectional communication device, such as a gigabit ethernettransceiver. The particular exemplary implementation chosen is depictedin FIG. 1, which is a simplified block diagram of a multi-paircommunication system operating in conformance with the IEEE 802.3abstandard for one gigabit (Gb/s) Ethernet full-duplex communication overfour twisted pairs of Category-5 copper wires.

The communication system illustrated in FIG. 1 is represented as apoint-to-point system, in order to simplify the explanation, andincludes two main transceiver blocks 102 and 104, coupled together withfour twisted-pair cables. Each of the wire pairs is coupled between thetransceiver blocks through a respective one of four line interfacecircuits 106 and communicate information developed by respective ones offour transmitter/receiver circuits (constituent transceivers) 108coupled between respective interface circuits and a physical codingsublayer (PCS) block 110. Four constituent transceivers 108 are capableof operating simultaneously at 250 megabits per second (Mb/s), and arecoupled through respective interface circuits to facilitate full-duplexbidirectional operation. Thus, one Gb/s communication throughput of eachof the transceiver blocks 102 and 104 is achieved by using four 250 Mb/s(125 Megabaud at 2 bits per symbol) constituent transceivers 108 foreach of the transceiver blocks and four twisted pairs of copper cablesto connect the two transceivers together.

The exemplary communication system of FIG. 1 has a superficialresemblance to a 100BASE-T4 system, but is configured to operate at 10times the bit rate. As such, it should be understood that certain systemperformance characteristics, such as sampling rates and the like, willbe consequently higher causing lengthy and complex computations to beperformed during increasingly shorter periods of time. At gigabit datarates over potentially noisy channels, a proportionately greater degreeof signal processing is required in many instances to ensure an adequatedegree of signal fidelity and quality.

FIG. 2 is a simplified block diagram of the functional architecture andinternal construction of an exemplary transceiver block, indicatedgenerally at 200, such as transceiver 102 of FIG. 1. Since theillustrated transceiver application relates to gigabit ethernettransmission, the transceiver will be referred to as the “gigabittransceiver”. For ease of illustration and description, FIG. 2 showsonly one of the four 250 Mb/s constituent transceivers which areoperating simultaneously (termed herein 4-D operation). However, sincethe operation of the four constituent transceivers are necessarilyinterrelated, certain blocks in the signal lines in the exemplaryembodiment of FIG. 2 perform and carry 4-dimensional (4-D) functions and4-D signals, respectively. By 4-D, it is meant that the data from thefour constituent transceivers are used simultaneously. In order toclarify signal relationships in FIG. 2, thin lines correspond to1-dimensional functions or signals (i.e., relating to only a singletransceiver), and thick lines correspond to 4-D functions or signals(relating to all four transceivers).

With reference to FIG. 2, the gigabit transceiver 200 includes a GigabitMedium Independent Interface (GMII) block 202, a Physical CodingSublayer (PCS) block 204, a pulse shaping filter 206, adigital-to-analog (D/A) converter 208, a line interface block 210, ahighpass filter 212, a programmable gain amplifier (PGA) 214, ananalog-to-digital (A/D) converter 216, an automatic gain control block220, a timing recovery block 222, a pair-swap multiplexer block 224, ademodulator 226, an offset canceler 228, a near-end crosstalk (NEXT)canceler block 230 having three NEXT cancelers, and an echo canceler232. The gigabit transceiver 200 also includes an A/D first-in-first-outbuffer (FIFO) 218 to facilitate proper transfer of data from the analogclock region to the receive clock region, and a FIFO block 234 tofacilitate proper transfer of data from the transmit clock region to thereceive clock region. The gigabit transceiver 200 can optionally includea filter to cancel far-end crosstalk noise (FEXT canceler).

On the transmit path, the transmit section of the GMII block 202receives data from a Media Access Control (MAC) module (not shown inFIG. 2) and passes the digital data to the transmit section 204T of thePCS block 204 via a FIFO 201 in byte-wide format at the rate of 125 MHz.The FIFO 201 is essentially a synchronization buffer device and isprovided to ensure proper data transfer from the MAC layer to thePhysical Coding (PHY) layer, since the transmit clock of the PHY layeris not necessarily synchronized with the clock of the MAC layer. Thissmall FIFO 201 can be constructed with from three to five memory cellsto accommodate the elasticity requirement which is a function of framesize and frequency offset.

The transmit section 204T of the PCS block 204 performs scrambling andcoding of the data and other control functions. Transmit section 204T ofthe PCS block 204 generates four 1D symbols, one for each of the fourconstituent transceivers. The 1D symbol generated for the constituenttransceiver depicted in FIG. 2 is filtered by a partial response pulseshaping filter 206 so that the radiated emission of the output of thetransceiver may fall within the EMI requirements of the FederalCommunications Commission. The pulse shaping filter 206 is constructedwith a transfer function 0.75+0.25 z⁻¹, such that the power spectrum ofthe output of the transceiver falls below the power spectrum of a100Base-Tx signal. The 100Base-Tx is a widely used and accepted FastEthernet standard for 100 Mb/s operation on two pairs of category-5twisted pair cables. The output of the pulse shaping filter 206 isconverted to an analog signal by the D/A converter 208 operating at 125MHz. The analog signal passes through the line interface block 210, andis placed on the corresponding twisted pair cable for communication to aremote receiver.

On the receive path, the line interface block 210 receives an analogsignal from the twisted pair cable. The received analog signal ispreconditioned by a highpass filter 212 and a programmable gainamplifier (PGA) 214 before being converted to a digital signal by theA/D converter 216 operating at a sampling rate of 125 MHz. Sample timingof the A/D converter 216 is controlled by the output of a timingrecovery block 222 controlled, in turn, by decision and error signalsfrom a demodulator 226. The resulting digital signal is properlytransferred from the analog clock region to the receive clock region byan A/D FIFO 218, an output of which is also used by an automatic gaincontrol circuit 220 to control the operation of the PGA 214.

The output of the A/D FIFO 218, along with the outputs from the A/DFIFOs of the other three constituent transceivers are inputted to apair-swap multiplexer block 224. The pair-swap multiplexer block 224 isoperatively responsive to a 4D pair-swap control signal, asserted by thereceive section 204R of PCS block 204, to sort out the 4 input signalsand send the correct signals to the respective demodulators of the 4constituent transceivers. Since the coding scheme used for the gigabittransceivers 102, 104 (referring to FIG. 1) is based on the fact thateach twisted pair of wire corresponds to a 1D constellation, and thatthe four twisted pairs, collectively, form a 4D constellation, forsymbol decoding to function properly, each of the four twisted pairsmust be uniquely identified with one of the four dimensions. Anyundetected swapping of the four pairs would necessarily result inerroneous decoding. Although described as performed by the receivesection 204R of PCS block 204 and the pair-swap multiplexer block 224,in the exemplary embodiment of FIG. 2, the pair-swapping control mightalternatively be performed by the demodulator 226.

Demodulator 226 receives the particular received signal 2 intended forit from the pair-swap multiplexer block 224, and functions to demodulateand decode the signal prior to directing the decoded symbols to the PCSlayer 204 for transfer to the MAC. The demodulator 226 includes amulti-component feedforward equalizer (FFE) 26, having its outputcoupled to a de-skew memory circuit 36 and a trellis decoder 38. The FFE26 is multi-component in the sense that it includes a pulse shapingfilter 28, a programmable inverse partial response (IPR) filter 30, asumming device 32, and an adaptive gain stage 34. Functionally, the FFE26 might be characterized as a least-mean-squares (LMS) type adaptivefilter which performs channel equalization as described in thefollowing.

Pulse shaping filter 28 is coupled to receive an input signal 2 from thepair swap MUX 224 and functions to generate a precursor to the inputsignal 2. Used for timing recovery, the precursor might be aptlydescribed as a zero-crossing inserted at a precursor position of thesignal. Such a zero-crossing assists a timing recovery circuit indetermining phase relationships between signals, by giving the timingrecovery circuit an accurately determinable signal transition point foruse as a reference. The pulse shaping filter 28 can be placed anywherebefore the decoder block 38. In the exemplary embodiment of FIG. 2, thepulse shaping filter 28 is positioned at the input of the FFE 26.

The pulse shaping filter 28 transfer function may be represented by afunction of the form −γ+z⁻¹, with γ equal to {fraction (1/16)} for shortcables (less than 80 meters) and ⅛ for long cables (more than 80 m). Thedetermination of the length of a cable is based on the gain of thecoarse PGA section 14 of the PGA 214.

A programmable inverse partial response (IPR) filter 30 is coupled toreceive the output of the pulse shaping filter 28, and functions tocompensate the ISI introduced by the partial response pulse shaping inthe transmitter section of the remote transceiver which transmitted theanalog equivalent of the digital signal 2. The IPR filter 30 transferfunction may be represented by a function of the form 1/(1+Kz⁻¹) and mayalso be described as dynamic. In particular, the filter's K value isdynamically varied from an initial non-zero setting, valid at systemstart-up, to a final setting. K may take any positive value strictlyless than 1. In the illustrated embodiment, K might take on a value ofabout 0.484375 during startup, and be dynamically ramped down to zeroafter convergence of the decision feedback equalizer included inside thetrellis decoder 38.

The foregoing is particularly advantageous in high-speed data recoverysystems, since by compensating the transmitter induced ISI at start-up,prior to decoding, it reduces the amount of processing required by thedecoder to that required only for compensating transmission channelinduced ISI. This “bifurcated” or divided ISI compensation processallows for fast acquisition in a robust and reliable manner. After DFEconvergence, noise enhancement in the feedforward equalizer 26 isavoided by dynamically ramping the feedback gain factor K of the IPRfilter 30 to zero, effectively removing the filter from the activecomputational path.

A summing device 32 subtracts from the output of the IPR filter 30 thesignals received from the offset canceler 228, the NEXT cancelers 230,and the echo canceler 232. The offset canceler 228 is an adaptive filterwhich generates an estimate of the offset introduced at the analog frontend which includes the PGA 214 and the A/D converter 216. Likewise, thethree NEXT cancelers 230 are adaptive filters used for modeling the NEXTimpairments in the received signal caused by the symbols sent by thethree local transmitters of the other three constituent transceivers.The impairments are due to a near-end crosstalk mechanism between thepairs of cables. Since each receiver has access to the data transmittedby the other three local transmitters, it is possible to nearlyreplicate the NEXT impairments through filtering. Referring to FIG. 2,the three NEXT cancelers 230 filter the signals sent by the PCS block204 to the other three local transmitters and produce three signalsreplicating the respective NEXT impairments. By subtracting these threesignals from the output of the IPR filter 30, the NEXT impairments areapproximately canceled.

Due to the bi-directional nature of the channel, each local transmittercauses an echo impairment on the received signal of the local receiverwith which it is paired to form a constituent transceiver. The echocanceler 232 is an adaptive filter used for modeling the echoimpairment. The echo canceler 232 filters the signal sent by the PCSblock 204 to the local transmitter associated with the receiver, andproduces a replica of the echo impairment. By subtracting this replicasignal from the output of the IPR filter 30, the echo impairment isapproximately canceled.

Following NEXT, echo and offset cancellation, the signal is coupled toan adaptive gain stage 34 which functions to fine tune the gain of thesignal path using a zero-forcing LMS algorithm. Since this adaptive gainstage 34 trains on the basis of errors of the adaptive offset, NEXT andecho cancellation filters 228, 230 and 232 respectively, it provides amore accurate signal gain than the PGA 214.

The output of the adaptive gain stage 34, which is also the output ofthe FFE 26, is inputted to a de-skew memory 36. The de-skew memory 36 isa four-dimensional function block, i.e., it also receives the outputs ofthe three FFEs of the other three constituent transceivers as well asthe output of FFE 26 illustrated in FIG. 2. There may be a relative skewin the outputs of the 4 FFEs, which are the 4 signal samplesrepresenting the 4 symbols to be decoded. This relative skew can be upto 50 nanoseconds, and is due to the variations in the way the copperwire pairs are twisted. In order to correctly decode the four symbols,the four signal samples must be properly aligned. The de-skew memory isresponsive to a 4D de-skew control signal asserted by the PCS block 204to de-skew and align the four signal samples received from the fourFFEs. The four de-skewed signal samples are then directed to the trellisdecoder 38 for decoding.

Data received at the local transceiver was encoded, prior totransmission by a remote transceiver, using an 8-state four-dimensionaltrellis code. In the absence of inter-symbol interference (ISI), aproper 8-state Viterbi decoder would provide optimal decoding of thiscode. However, in the case of Gigabit Ethernet, the Category-5 twistedpair cable introduces a significant amount of ISI. In addition, as wasdescribed above in connection with the FFE stage 26, the partialresponse filter of the remote transmitter on the other end of thecommunication channel also contributes a certain component of ISI.Therefore, during nominal operation, the trellis decoder 38 must decodeboth the trellis code and compensate for at least transmission channelinduced ISI, at a substantially high computational rate, correspondingto a symbol rate of about 125 Mhz.

In the illustrated embodiment of the gigabit transceiver of FIG. 2, thetrellis decoder 38 suitably includes an 8-state Viterbi decoder forsymbol decoding, and incorporates circuitry which implements adecision-feedback sequence estimation approach in order to compensatethe ISI components perturbing the signal which represents transmittedsymbols. The 4D output 40 of the trellis decoder 38 is provided to thereceive section 204R of the PCS block. The receive section 204R of PCSblock de-scrambles and further decodes the symbol stream and then passesthe decoded packets and idle stream to the receive section of the GMIIblock 202 for transfer to the MAC module.

The 4D outputs 42 and 44, which represent the error and tentativedecision signals defined by the decoder, respectively, are provided tothe timing recovery block 222, whose output controls the sampling timeof the A/D converter 216. One of the four components of the error 42 andone of the four components of the tentative decision 44 correspond tothe signal stream pertinent to the particular receiver section,illustrated in FIG. 2, and are provided to the adaptive gain stage 34 toadjust the gain of the signal path.

The component 42A of the 4D error 42, which corresponds to the receivershown in FIG. 2, is further provided to the adaptation circuitry of eachof the adaptive offset, NEXT and echo cancellation filters 228, 230,232. Adaptation circuitry evaluates the content of the error componentand, initially, adapts the filter's training process to develop suitablefilter coefficient values. During nominal operation, adaptationcircuitry monitors the error component and provides periodic updates tothe filter coefficients in response thereto.

As implemented in the exemplary Ethernet gigabit transceiver, thetrellis decoder 38 functions to decode symbols that have been encoded inaccordance with the trellis code specified in the IEEE 802.3ab standard(1000BASE-T, or gigabit). As mentioned above, information signals arecommunicated between transceivers at a symbol rate of about 125 Mhz, oneach of the pairs of twisted copper cables that make up the transmissionchannel. In accordance with established Ethernet communicationprotocols, information signals are modulated for transmission inaccordance with a 5-level Pulse Amplitude Modulation (PAM-5) modulationscheme. Thus, since information signals are represented by fiveamplitude levels, it will be understood that symbols can be expressed ina three bit representation on each twisted wire pair.

Turning now to FIGS. 4A and 4B, an exemplary PAM-5 constellation isdepicted in FIG. 4A which also depicts the one-dimensional symbol subsetpartitioning within the constellation. As illustrated in FIG. 4A, theconstellation is a representation of five amplitude levels, +2, +1, 0,−1, −2, in decreasing order. Symbol subset partitioning occurs bydividing the five levels into two 1D subsets, X and Y, and assigning Xand Y subset designations to the five levels on an alternating basis.Thus +2, 0 and −2 are assigned to the Y subset; +1 and −1 are assignedto the X subset. The partitioning could, of course, be reversed, with +1and −1 being assigned a Y designation.

It should be recognized that although the X and Y subsets representdifferent absolute amplitude levels, the vector distance betweenneighboring amplitudes within the subsets are the same, i.e., two (2).The X subset therefore includes amplitude level designations whichdiffer by a value of two, (−1, +1), as does the Y subset (−2, 0, +2).This partitioning offers certain advantages to slicer circuitry in adecoder, as will be developed further below.

In FIG. 4B, the 1D subsets have been combined into 4D subsetsrepresenting the four twisted pairs of the transmission channel. Since1D subset definition is binary (X:Y) and there are four wire pairs,there are sixteen possible combinations of 4D subsets. These sixteenpossible combinations are assigned into eight 4D subsets, s0 to s7inclusive, in accordance with a trellis coding scheme. Each of the 4Dsubsets (also termed code subsets) are constructed of a union of twocomplementary 4D sub-subsets, e.g., code-subset three (identified as s3)is the union of sub-subset X:X:Y:X and its complementary image Y:Y:X:Y.

Data being processed for transmission is encoded using the abovedescribed 4-dimensional (4D) 8-state trellis code, in an encodercircuit, such as illustrated in the exemplary block diagram of FIG. 3,according to an encoding algorithm specified in the 1000BASE-T standard.Referring to FIG. 3, an exemplary encoder 300, which is commonlyprovided in the transmit PCS portion of a gigabit transceiver, might berepresented in simplified form as a convolutional encoder 302 incombination with a signal mapper 304. Data received by the transmit PCSfrom the MAC module via the transmit gigabit medium independentinterface are encoded with control data and scrambled, resulting in aneight bit data word represented by input bits D₀ through D₇ which areintroduced to the signal mapper 304 of the encoder 300 at a data rate ofabout 125 MHz. The two least significant bits, D₀ and D₁, are alsoinputted, in parallel fashion, into a convolutional encoder 302,implemented as a linear feedback shift register, in order to generate aredundancy bit C which is a necessary condition for the provision of thecoding gain of the code.

As described above, the convolutional encoder 302 is a linear feedbackshift register, constructed of three delay elements 303, 304 and 305(conventionally denoted by z⁻¹) interspersed with and separated by twosumming circuits 307 and 308 which function to combine the two leastsignificant bits (LSBs), D₀ and D₁, of the input word with the output ofthe first and second delay elements, 303 and 304 respectively. The twotime sequences formed by the streams of the two LSBs are convolved withthe coefficients of the linear feedback shift register to produce thetime sequence of the redundancy bit C. Thus, the convolutional encodermight be viewed as a state machine.

The signal mapper 304 maps the 9 bits (D₀-D₇ and C) into a particular4-dimensional constellation point. Each of the four dimensions uniquelycorresponds to one of the four twisted wire pairs. In each dimension,the possible symbols are from the symbol set {−2, −1, 0, +1, +2}. Thesymbol set is partitioned into two disjoint symbol subsets X and Y, withX={−1, +1} and Y={−2, 0, +2}, as described above and shown in FIG. 4A.

Referring to FIG. 4B, the eight code subsets s0 through s7 define theconstellation of the code in the signal space. Each of the code subsetsis formed by the union of two code sub-subsets, each of the codesub-subsets being formed by 4D patterns obtained from concatenation ofsymbols taken from the symbol subsets X and Y. For example, the codesubset s0 is formed by the union of the 4D patterns from the 4D codesub-subsets XXXX and YYYY. It should be noted that the distance betweenany two arbitrary even (respectively, odd) code-subsets is {square rootover (2)}. It should be further noted that each of the code subsets isable to define at least 72 constellation points. However, only 64constellation points in each code subset are recognized as codewords ofthe trellis code specified in the 1000BASE-T standard.

This reduced constellation is termed the pruned constellation.Hereinafter, the term “codeword” is used to indicate a 4D symbol thatbelongs to the pruned constellation. A valid codeword is part of a validpath in the trellis diagram.

Referring now to FIG. 3 and with reference to FIGS. 4A and 4B, inoperation, the signal mapper 304 uses the 3 bits D₁, D₀ and C to selectone of the code subsets s0-s7, and uses the 6 MSB bits of the inputsignal, D₂-D₇ to select one of 64 particular points in the selected codesubset. These 64 particular points of the selected coded subsetcorrespond to codewords of the trellis code. The signal mapper 304outputs the selected 4D constellation point 306 which will be placed onthe four twisted wire pairs after pulse shape filtering anddigital-to-analog conversion.

FIG. 5 shows the trellis diagram for the trellis code specified in the1000BASE-T standard. In the trellis diagram, each vertical column ofnodes represents the possible states that the encoder 300 (FIG. 3) canassume at a point in time. It is noted that the states of the encoder300 are dictated by the states of the convolutional encoder 302 (FIG.3). Since the convolutional encoder 302 has three delay elements, thereare eight distinct states. Successive columns of nodes represent thepossible states that might be defined by the convolutional encoder statemachine at successive points in time.

Referring to FIG. 5, the eight distinct states of the encoder 300 areidentified by numerals 0 through 7, inclusive. From any given currentstate, each subsequent transmitted 4D symbol must correspond to atransition of the encoder 300 from the given state to a permissiblesuccessor state. For example, from the current state 0 (respectively,from current states 2, 4, 6), a transmitted 4D symbol taken from thecode subset s0 corresponds to a transition to the successor state 0(respectively, to successor states 1, 2 or 3). Similarly, from currentstate 0, a transmitted 4D symbol taken from code subset s2(respectively, code subsets s4, s6) corresponds to a transition tosuccessor state 1 (respectively, successor states 2, 3).

Familiarity with the trellis diagram of FIG. 5, illustrates that fromany even state (i.e., states 0, 2, 4 or 6), valid transitions can onlybe made to certain ones of the successor states, i.e., states 0, 1, 2 or3. From any odd state (states 1, 3, 5 or 7), valid transitions can onlybe made to the remaining successor states, i.e., states 4, 5, 6 or 7.Each transition in the trellis diagram, also called a branch, may bethought of as being characterized by the predecessor state (the state itleaves), the successor state (the state it enters) and the correspondingtransmitted 4D symbol. A valid sequence of states is represented by apath through the trellis which follows the above noted rules. A validsequence of states corresponds to a valid sequence of transmitted 4Dsymbols.

At the receiving end of the communication channel, the trellis decoder38 uses the methodology represented by the trellis diagram of FIG. 5 todecode a sequence of received signal samples into their symbolicrepresentation, in accordance with the well known Viterbi algorithm. Atraditional Viterbi decoder processes information signals iteratively,on an information frame by information frame basis (in the GigabitEthernet case, each information frame is a 4D received signal samplecorresponding to a 4D symbol), tracing through a trellis diagramcorresponding to the one used by the encoder, in an attempt to emulatethe encoder's behavior. At any particular frame time, the decoder is notinstantaneously aware of which node (or state) the encoder has reached,thus, it does not try to decode the node at that particular frame time.Instead, given the received sequence of signal samples, the decodercalculates the most likely path to every node and determines thedistance between each of such paths and the received sequence in orderto determine a quantity called the path metric.

In the next frame time, the decoder determines the most likely path toeach of the new nodes of that frame time. To get to any one of the newnodes, a path must pass through one of the old nodes. Possible paths toeach new node are obtained by extending to this new node each of the oldpaths that are allowed to be thus extended, as specified by the trellisdiagram. In the trellis diagram of FIG. 5, there are four possible pathsto each new node. For each new node, the extended path with the smallestpath metric is selected as the most likely path to this new node.

By continuing the above path-extending process, the decoder determines aset of surviving paths to the set of nodes at the nth frame time. If allof the paths pass through the same node at the first frame time, thenthe traditional decoder knows which most likely node the encoder enteredat the first frame time, regardless of which node the encoder entered atthe nth frame time. In other words, the decoder knows how to decode thereceived information associated with the first frame time, even thoughit has not yet made a decision for the received information associatedwith the nth frame time. At the nth frame time, the traditional decoderexamines all surviving paths to see if they pass through the same firstbranch in the first frame time. If they do, then the valid symbolassociated with this first branch is outputted by the decoder as thedecoded information frame for the first frame time. Then, the decoderdrops the first frame and takes in a new frame for the next iteration.Again, if all surviving paths pass through the same node of the oldestsurviving frame, then this information frame is decoded. The decodercontinues this frame-by-frame decoding process indefinitely so long asinformation is received.

The number of symbols that the decoder can store is called thedecoding-window width. The decoder must have a decoding window widthlarge enough to ensure that a well-defined decision will almost alwaysbe made at a frame time. As discussed later in connection with FIGS. 13and 14, the decoding window width of the trellis decoder 38 of FIG. 2 is10 symbols. This length of the decoding window is selected based onresults of computer simulation of the trellis decoder 38.

A decoding failure occurs when not all of the surviving paths to the setof nodes at frame time n pass through a common first branch at frametime 0. In such a case, the traditional decoder would defer making adecision and would continue tracing deeper in the trellis. This wouldcause unacceptable latency for a high-speed system such as the gigabitEthernet transceiver. Unlike the traditional decoder, the trellisdecoder 38 of the present invention does not check whether the survivingpaths pass through a common first branch. Rather, the trellis decoder,in accordance with the invention, makes an assumption that the survivingpaths at frame time n pass through such a branch, and outputs a decisionfor frame time 0 on the basis of that assumption. If this decision isincorrect, the trellis decoder 38 will necessarily output a fewadditional incorrect decisions based on the initial perturbation, butwill soon recover due to the nature of the particular relationshipbetween the code and the characteristics of the transmission channel. Itshould, further, be noted that this potential error introduction sourceis relatively trivial in actual practice, since the assumption made bythe trellis decoder 38 that all the surviving paths at frame time n passthrough a common first branch at frame time 0 is a correct one to a veryhigh statistical probability.

FIG. 6 is a simplified block diagram of the construction details of anexemplary trellis decoder such as described in connection with FIG. 2.The exemplary trellis decoder (again indicated generally at 38) isconstructed to include a multiple decision feedback equalizer (MDFE)602, Viterbi decoder circuitry 604, a path metrics module 606, a pathmemory module 608, a select logic 610, and a decision feedback equalizer612. In general, a Viterbi decoder is often thought of as including thepath metrics module and the path memory module. However, because of theunique arrangement and functional operation of the elements of theexemplary trellis decoder 38, the functional element which performs theslicing operation will be referred to herein as Viterbi decodercircuitry, a Viterbi decoder, or colloquially a Viterbi.

The Viterbi decoder circuitry 604 performs 4D slicing of signalsreceived at the Viterbi inputs 614, and computes the branch metrics. Abranch metric, as the term is used herein, is well known and refers toan elemental path between neighboring Trellis nodes. A plurality ofbranch metrics will thus be understood to make up a path metric. Anextended path metric will be understood to refer to a path metric, whichis extended by a next branch metric to thereby form an extension to thepath. Based on the branch metrics and the previous path metricsinformation 618 received from the path metrics module 606, the Viterbidecoder 604 extends the paths and computes the extended path metrics 620which are returned to the path metrics module 606. The Viterbi decoder604 selects the best path incoming to each of the eight states, updatesthe path memory stored in the path memory module 608 and the pathmetrics stored in the path metrics module 606.

In the traditional Viterbi decoding algorithm, the inputs to a decoderare the same for all the states of the code. Thus, a traditional Viterbidecoder would have only one 4D input for a 4D 8-state code. In contrast,and in accordance with the present invention, the inputs 614 to theViterbi decoder 604 are different for each of the eight states. This isthe result of the fact the Viterbi inputs 614 are defined by feedbacksignals generated by the MDFE 602 and are different for each of theeight paths (one path per state) of the Viterbi decoder 604, as will bediscussed later.

There are eight Viterbi inputs 614 and eight Viterbi decisions 616, eachcorresponding to a respective one of the eight states of the code. Eachof the eight Viterbi inputs 614, and each of the decision outputs 618,is a 4-dimensional vector whose four components are the Viterbi inputsand decision outputs for the four constituent transceivers,respectively. In other words, the four components of each of the eightViterbi inputs 614 are associated with the four pairs of the Category-5cable. The four components are a received word that corresponds to avalid codeword. From the foregoing, it should be understood thatdetection (decoding, demodulation, and the like) of information signalsin a gigabit system is inherently computationally intensive. When it isfurther realized that received information must be detected at a veryhigh speed and in the presence of ISI channel impairments, thedifficulty in achieving robust and reliable signal detection will becomeapparent.

In accordance with the present invention, the Viterbi decoder 604detects a non-binary word by first producing a set of one-dimensional(1D) decisions and a corresponding set of 1D errors from the 4D inputs.By combining the 1D decisions with the 1D errors, the decoder produces aset of 4D decisions and a corresponding set of 4D errors. Hereinafter,this generation of 4D decisions and errors from the 4D inputs isreferred to as 4D slicing. Each of the 1D errors represents the distancemetric between one 1D component of the eight 4D-inputs and a symbol inone of the two disjoint symbol-subsets X, Y. Each of the 4D errors isthe distance between the received word and the corresponding 4D decisionwhich is a codeword nearest to the received word with respect to one ofthe code-subsets si, where i=0, . . . 7.

4D errors may also be characterized as the branch metrics in the Viterbialgorithm. The branch metrics are added to the previous values of pathmetrics 618 received from the path metrics module 606 to form theextended path metrics 620 which are then stored in the path metricsmodule 606, replacing the previous path metrics. For any one given stateof the eight states of the code, there are four incoming paths. For agiven state, the Viterbi decoder 604 selects the best path, i.e., thepath having the lowest metric of the four paths incoming to that state,and discards the other three paths. The best path is saved in the pathmemory module 608. The metric associated with the best path is stored inthe path metrics module 606, replacing the previous value of the pathmetric stored in that module.

In the following, the 4D slicing function of the Viterbi decoder 604will be described in detail. 4D slicing may be described as beingperformed in three sequential steps. In a first step, a set of 1Ddecisions and corresponding 1D errors are generated from the 4D Viterbiinputs. Next, the 1D decisions and 1D errors are combined to form a setof 2D decisions and corresponding 2D errors. Finally, the 2D decisionsand 2D errors are combined to form 4D decisions and corresponding 4Derrors.

FIG. 7 is a simplified, conceptual block diagram of a first exemplaryembodiment of a 1D slicing function such as might be implemented by theViterbi decoder 604 of FIG. 6. Referring to FIG. 7, a 1D component 702of the eight 4D Viterbi inputs (614 of FIG. 6) is sliced, i.e.,detected, in parallel fashion, by a pair of 1D slicers 704 and 706 withrespect to the X and Y symbol-subsets. Each slicer 704 and 706 outputs arespective 1D decision 708 and 710 with respect to the appropriaterespective symbol-subset X, Y and an associated squared error value 712and 714. Each 1D decision 708 or 710 is the symbol which is closest tothe 1D input 702 in the appropriate symbol-subset X and Y, respectively.The squared error values 712 and 714 each represent the square of thedifference between the 1D input 702 and their respective 1D decisions708 and 710.

The 1D slicing function shown in FIG. 7 is performed for all fourconstituent transceivers and for all eight states of the trellis code inorder to produce one pair of 1D decisions per transceiver and per state.Thus, the Viterbi decoder 604 has a total of 32 pairs of 1D slicersdisposed in a manner identical to the pair of slicers 704, 706illustrated in FIG. 7.

FIG. 8 is a simplified block diagram of a second exemplary embodiment ofcircuitry capable of implementing a 1D slicing function suitable forincorporation in the Viterbi decoder 604 of FIG. 5. Referring to FIG. 8,the 1D component 702 of the eight 4D Viterbi inputs is sliced, i.e.,detected, by a first pair of 1D slicers 704 and 706, with respect to theX and Y symbol-subsets, and also by a 5-level slicer 805 with respect tothe symbol set which represents the five levels (+2, +1, 0, −1, −2) ofthe constellation, i.e., a union of the X and Y symbol-subsets. As inthe previous case described in connection with FIG. 7, the slicers 704and 706 output 1D decisions 708 and 710. The 1D decision 708 is thesymbol which is nearest the 1D input 702 in the symbol-subset X, while1D decision 710 corresponds to the symbol which is nearest the 1D input702 in the symbol-subset Y. The output 807 of the 5-level slicer 805corresponds to the particular one of the five constellation symbolswhich is determined to be closest to the 1D input 702.

The difference between each decision 708 and 710 and the 5-level sliceroutput 807 is processed, in a manner to be described in greater detailbelow, to generate respective quasi-squared error terms 812 and 814. Incontrast to the 1D error terms 712, 714 obtained with the firstexemplary embodiment of a 1D slicer depicted in FIG. 7, the 1D errorterms 812, 814 generated by the exemplary embodiment of FIG. 8 are moreeasily adapted to discerning relative differences between a 1D decisionand a 1D Viterbi input.

In particular, the slicer embodiment of FIG. 7 may be viewed asperforming a “soft decode”, with 1D error terms 712 and 714 representedby Euclidian metrics. The slicer embodiment depicted in FIG. 8 may beviewed as performing a “hard decode”, with its respective 1D error terms812 and 814 expressed in Hamming metrics (i.e., 1 or 0). Thus, there isless ambiguity as to whether the 1D Viterbi input is closer to the Xsymbol subset or to the Y symbol subset. Furthermore, Hamming metricscan be expressed in a fewer number of bits, than Euclidian metrics,resulting in a system that is substantially less computationally complexand substantially faster.

In the exemplary embodiment of FIG. 8, error terms are generated bycombining the output of the five level slicer 805 with the outputs ofthe 1D slicers 704 and 706 in respective adder circuits 809A and 809B.The outputs of the adders are directed to respective squared magnitudeblocks 811A and 811B which generate the binary squared error terms 812and 814, respectively.

Implementation of squared error terms by use of circuit elements such asadders 809A, 809B and the magnitude squared blocks 811A, 811B is donefor descriptive convenience and conceptual illustration purposes only.In practice, squared error term definition is implemented with a look-uptable that contains possible values for error-X and error-Y for a givenset of decision-X, decision-Y and Viterbi input values. The look-uptable can be implemented with a read-only-memory device oralternatively, a random logic device or PLA. Examples of look-up tables,suitable for use in practice of the present invention, are illustratedin FIGS. 17, 18A and 18B.

The 1D slicing function exemplified in FIG. 8 is performed for all fourconstituent transceivers and for all eight states of the trellis code inorder to produce one pair of 1D decisions per transceiver and per state.Thus, the Viterbi decoder 604 has a total of thirty two pairs of 1Dslicers that correspond to the pair of slicers 704, 706, and thirty two5-level slicers that correspond to the 5-level slicer 805 of FIG. 8.

Each of the 1D errors is represented by substantially fewer bits thaneach 1D component of the 4D inputs. For example, in the embodiment ofFIG. 7, the 1D component of the 4D Viterbi input is represented by 5bits, while the 1D error is represented by 2 or 3 bits. Traditionally,proper soft decision decoding of such a trellis code would require thatthe distance metric (Euclidean distance) be represented by 6 to 8 bits.One advantageous feature of the present invention is that only 2 or 3bits are required for the distance metric in soft decision decoding ofthis trellis code.

In the embodiment of FIG. 8, the 1D error can be represented by just 1bit. It is noted that, since the 1D error is represented by 1 bit, thedistance metric used in this trellis decoding is no longer the Euclideandistance, which is usually associated with trellis decoding, but isinstead the Hamming distance, which is usually associated with harddecision decoding of binary codewords. This is another particularlyadvantageous feature of the present invention.

FIG. 9 is a block diagram illustrating the generation of the 2D errorsfrom the 1D errors for twisted pairs A and B (corresponding toconstituent transceivers A and B). Since the generation of errors issimilar for twisted pairs C and D, this discussion will only concernitself with the A:B 2D case. It will be understood that the discussionis equally applicable to the C:D 2D case with the appropriate change innotation. Referring to FIG. 9, 1D error signals 712A, 712B, 714A, 714Bmight be produced by the exemplary 1D slicing functional blocks shown inFIGS. 7 or 8. The 1D error term signal 712A (or respectively, 712B) isobtained by slicing, with respect to symbol-subset X, the 1D componentof the 4D Viterbi input, which corresponds to pair A (or respectively,pair B). The 1D error term 714A (respectively, 714B) is obtained byslicing, with respect to symbol-subset Y, the 1D component of the 4DViterbi input, which corresponds to pair A (respectively, B). The 1Derrors 712A, 712B, 714A, 714B are added according to all possiblecombinations (XX, XY, YX and YY) to produce 2D error terms 902AB, 904AB,906AB, 908AB for pairs A and B. Similarly, the 1D errors 712C, 712D,714C, 714D (not shown) are added according to the four differentsymbol-subset combinations XX, XY, YX and YY) to produce corresponding2D error terms for wire pairs C and D.

FIG. 10 is a block diagram illustrating the generation of the 4D errorsand extended path metrics for the four extended paths outgoing fromstate 0. Referring to FIG. 10, the 2D errors 902AB, 902CD, 904AB, 904CD,906AB, 906CD, 908AB, 908CD are added in pairs according to eightdifferent combinations to produce eight intermediate 4D errors 1002,1004, 1006, 1008, 1010, 1012, 1014, 1016. For example, the 2D error902AB, which is the squared error with respect to XX from pairs A and B,are added to the 2D error 902CD, which is the squared error with respectto XX from pairs C and D, to form the intermediate 4D error 1002 whichis the squared error with respect to sub-subset XXXX for pairs A, B, Cand D. Similarly, the intermediate 4D error 1004 which corresponds tothe squared error with respect to sub-subset YYYY is formed from the 2Derrors 908AB and 908CD.

The eight intermediate 4D errors are grouped in pairs to correspond tothe code subsets s0, s2, s4, and s6 represented in FIG. 4B. For example,the intermediate 4D errors 1002 and 1004 are grouped together tocorrespond to the code subset s0 which is formed by the union of theXXXX and YYYY sub-subsets. From each pair of intermediate 4D errors, theone with the lowest value is selected (the other one being discarded) inorder to provide the branch metric of a transition in the trellisdiagram from state 0 to a subsequent state. It is noted that, accordingto the trellis diagram, transitions from an even state (i.e., 0, 2, 4,and 6) are only allowed to be to the states 0, 1, 2, and 3, andtransitions from an odd state (i.e., 1, 3, 5, and 7) are only allowed tobe to the states 4, 5, 6 and 7. Each of the index signals 1026, 1028,1030, 1032 indicates which of the 2 sub-subsets the selectedintermediate 4D error corresponds to. The branch metrics 1018, 1020,1022, 1024 are the branch metrics for the transitions in the trellisdiagram of FIG. 5 associated with code-subsets s0, s2, s4, and s6respectively, from state 0 to states 0, 1, 2 and 3, respectively. Thebranch metrics are added to the previous path metric 1000 for state 0 inorder to produce the extended path metrics 1034, 1036, 1038, 1040 of thefour extended paths outgoing from state 0 to states 0, 1, 2 and 3,respectively.

Associated with the eight intermediate 4D errors 1002, 1004, 1006, 1008,1010, 1012, 1014, 1016 are the 4D decisions which are formed from the 1Ddecisions made by one of the exemplary slicer embodiments of FIG. 7 or8. Associated with the branch metrics 1018, 1020, 1022, 1024 are the 4Dsymbols derived by selecting the 4D decisions using the index outputs1026, 1028, 1030, 1032.

FIG. 11 shows the generation of the 4D symbols associated with thebranch metrics 1018, 1020, 1022, 1024. Referring to FIG. 11, the 1Ddecisions 708A, 708B, 708C, 708D are the 1D decisions with respect tosymbol-subset X (as shown in FIG. 7) for constituent transceivers A, B,C, D, respectively, and the 1D decisions 714A, 714B, 714C, 714D are the1D decisions with respect to symbol-subset Y for constituenttransceivers A, B, C and D, respectively. The 1D decisions areconcatenated according to the combinations which correspond to a left orright hand portion of the code subsets s0, s2, s4, and s6, as depictedin FIG. 4B. For example, the 1D decisions 708A, 708B, 708C, 708D areconcatenated to correspond to the left hand portion, XXXX, of the codesubset s0. The 4D decisions are grouped in pairs to correspond to theunion of symbol-subset portions making up the code subsets s0, s2, s4,and s6. In particular, the 4D decisions 1102 and 1104 are groupedtogether to correspond to the code subset s0 which is formed by theunion of the XXXX and YYYY subset portions.

Referring to FIG. 11, the pairs of 4D decisions are inputted to themultiplexers 1120, 1122, 1124, 1126 which receive the index signals1026, 1028, 1030, 1032 (FIG. 10) as select signals. Each of themultiplexers selects from a pair of the 4D decisions, the 4D decisionwhich corresponds to the sub-subset indicated by the corresponding indexsignal and outputs the selected 4D decision as the 4D symbol for thebranch whose branch metric is associated with the index signal. The 4Dsymbols 1130, 1132, 1134, 1136 correspond to the transitions in thetrellis diagram of FIG. 5 associated with code-subsets s0, s2, s4 and s6respectively, from state 0 to states 0, 1, 2 and 3, respectively. Eachof the 4D symbols 1130, 1132, 1134, 1136 is the codeword in thecorresponding code-subset (s0, s2, s4 and s6) which is closest to the 4DViterbi input for state 0 (there is a 4D Viterbi input for each state).The associated branch metric (FIG. 10) is the 4D squared distancebetween the codeword and the 4D Viterbi input for state 0.

FIG. 12 illustrates the selection of the best path incoming to state 0.The extended path metrics of the four paths incoming to state 0 fromstates 0, 2, 4 and 6 are inputted to the comparator module 1202 whichselects the best path, i.e., the path with the lowest path metric, andoutputs the Path 0 Select signal 1206 as an indicator of this pathselection, and the associated path metric 1204.

The procedure described above for processing a 4D Viterbi input forstate 0 of the code to obtain four branch metrics, four extended pathmetrics, and four corresponding 4D symbols is similar for the otherstates. For each of the other states, the selection of the best pathfrom the four incoming paths to that state is also similar to theprocedure described in connection with FIG. 12.

The above discussion of the computation of the branch metrics,illustrated by FIG. 7 through 11, is an exemplary application of themethod for slicing (detecting) a received L-dimensional word and forcomputing the distance of the received L-dimensional word from acodeword, for the particular case where L is equal to 4.

In general terms, i.e., for any value of L greater than 2, the methodcan be described as follows. The codewords of the trellis code areconstellation points chosen from 2^(L−1) code-subsets. A codeword is aconcatenation of L symbols selected from two disjoint symbol-subsets andis a constellation point belonging to one of the 2^(L−1) code-subsets.At the receiver, L inputs are received, each of the L inputs uniquelycorresponding to one of the L dimensions. The received word is formed bythe L inputs. To detect the received word, 2^(L−1) identical input setsare formed by assigning the same L inputs to each of the 2^(L−1) inputsets. Each of the L inputs of each of the 2^(L−1) input sets is slicedwith respect to each of the two disjoint symbol-subsets to produce anerror set of 2L one-dimensional errors for each of the 2^(L−1)code-subsets. For the particular case of the trellis code of the typedescribed by the trellis diagram of FIG. 5, the one-dimensional errorsare combined within each of the 2^(L−1) error sets to produce 2^(L−2)L-dimensional errors for the corresponding code-subset such that each ofthe 2^(L−2) L-dimensional errors is a distance between the received wordand one of the codewords in the corresponding code-subset.

One embodiment of this combining operation can be described as follows.First, the 2L one-dimensional errors are combined to produce 2Ltwo-dimensional errors (FIG. 9). Then, the 2L two-dimensional errors arecombined to produce 2^(L) intermediate L-dimensional errors which arearranged into 2^(L−1) pairs of errors such that these pairs of errorscorrespond one-to-one to the 2^(L−1) code-subsets (FIG. 10, signals 1002through 1016). A minimum is selected for each of the 2^(L−1) pairs oferrors (FIG. 10, signals 1026, 1028, 1030, 1032). These minima are the2^(L−1) L-dimensional errors. Due to the constraints on transitions fromone state to a successor state, as shown in the trellis diagram of FIG.5, only half of the 2^(L−1) L-dimensional errors correspond to allowedtransitions in the trellis diagram. These 2^(L−2) L-dimensional errorsare associated with 2^(L−2) L-dimensional decisions. Each of the 2^(L−2)L-dimensional decisions is a codeword closest in distance to thereceived word (the distance being represented by one of the 2^(L−2)L-dimensional errors), the codeword being in one of half of the 2^(L−1)code-subsets, i.e., in one of 2^(L−2) code-subsets of the 2^(L−1)code-subsets (due to the particular constraint of the trellis codedescribed by the trellis diagram of FIG. 5).

It is important to note that the details of the combining operation onthe 2L one-dimensional errors to produce the final L-dimensional errorsand the number of the final L-dimensional errors are functions of aparticular trellis code. In other words, they vary depending on theparticular trellis code.

FIG. 13 illustrates the construction of the path memory module 608 asimplemented in the embodiment of FIG. 6. The path memory module 608includes a path memory for each of the eight paths. In the illustratedembodiment of the invention, the path memory for each path isimplemented as a register stack, ten levels in depth. At each level, a4D symbol is stored in a register. The number of path memory levels ischosen as a tradeoff between receiver latency and detection accuracy.FIG. 13 only shows the path memory for path 0 and continues with theexample discussed in FIGS. 7-12. FIG. 13 illustrates how the 4D decisionfor the path 0 is stored in the path memory module 608, and how the Path0 Select signal, i.e., the information about which one of the fourincoming extended paths to state 0 was selected, is used in thecorresponding path memory to force merging of the paths at all depthlevels (levels 0 through 9) in the path memory.

Referring to FIG. 13, each of the ten levels of the path memory includesa 4-to-1 multiplexer (4:1 MUX) and a register to store a 4D decision.The registers are numbered according to their depth levels. For example,register 0 is at depth level 0. The Path 0 Select signal 1206 (FIG. 12)is used as the select input for the 4:1 MUXes 1302, 1304, 1306, . . . ,1320. The 4D decisions 1130, 1132, 1134, 1136 (FIG. 11) are inputted tothe 4:1 MUX 1302 which selects one of the four 4D decisions based on thePath 0 select signal 1206 and stores it in the register 0 of path 0. Onesymbol period later, the register 0 of path 0 outputs the selected 4Ddecision to the 4:1 MUX 1304. The other three 4D decisions inputted tothe 4:1 MUX 1304 are from the registers 0 of paths 2, 4, and 6. Based onthe Path 0 Select signal 1206, the 4:1 MUX 1304 selects one of the four4D decisions and stores it in the register 1 of path 0. One symbolperiod later, the register 1 of path 0 outputs the selected 4D decisionto the 4:1 MUX 1306. The other three 4D decisions inputted to the 4:1MUX 1306 are from the registers 1 of paths 2, 4, and 6. Based on thePath 0 Select signal 1206, the 4:1 MUX 1306 selects one of the four 4Ddecisions and stores it in the register 2 of path 0. This procedurecontinues for levels 3 through 9 of the path memory for path 0. Duringcontinuous operation, ten 4D symbols representing path 0 are stored inregisters 0 through 9 of the path memory for path 0.

Similarly to path 0, each of the paths 1 though 7 is stored as ten 4Dsymbols in the registers of the corresponding path memory. Theconnections between the MUX of one path and registers of different pathsfollows the trellis diagram of FIG. 2. For example, the MUX at level kfor path 1 receives as inputs the outputs of the registers at level k−1for paths 1, 3, 5, 7, and the MUX at level k for path 2 receives asinputs the outputs of the registers at level k−1 for paths 0, 2, 4, 6.

FIG. 14 is a block diagram illustrating the computation of the finaldecision and the tentative decisions in the path memory module 608 basedon the 4D symbols stored in the path memory for each state. At eachiteration of the Viterbi algorithm, the best of the eight states, i.e.,the one associated with the path having the lowest path metric, isselected, and the 4D symbol from the associated path stored at the lastlevel of the path memory is selected as the final decision 40 (FIG. 6).Symbols at lower depth levels are selected as tentative decisions, whichare used to feed the delay line of the DFE 612 (FIG. 6).

Referring to FIG. 14, the path metrics 1402 of the eight states,obtained from the procedure of FIG. 12, are inputted to the comparatormodule 1406 which selects the one with the lowest value and provides anindicator 1401 of this selection to the select inputs of the 8-to-1multiplexers (8:1 MUXes) 1402, 1404, 1406, . . . , 1420, which arelocated at path memory depth levels 0 through 9, respectively. Each ofthe 8:1 MUXes receives eight 4D symbols outputted from correspondingregisters for the eight paths, the corresponding registers being locatedat the same depth level as the MUX, and selects one of the eight 4Dsymbols to output, based on the select signal 1401. The outputs of the8:1 MUXes located at depth levels 0 through 9 are V₀, V₁, V₂, . . . ,V₉, respectively.

In the illustrated embodiment, one set of eight signals, output by thefirst register set (the register 0 set) to the first MUX 1402, is alsotaken off as a set of eight outputs, denoted V₀ ^(i) and provided to theMDFE (602 of FIG. 6) as a select signal which is used in a manner to bedescribed below. Although only the first register set is illustrated asproviding outputs to the DFE, the invention contemplates the second, oreven higher order, register sets also providing similar outputs. Incases where multiple register sets provide outputs, these are identifiedby the register set depth order as a subscript, as in V₁ ^(i), and thelike.

In the illustrated embodiment, the MUX outputs V₀, V₁, V₂ are delayed byone unit of time, and are then provided as the tentative decisionsV_(0F), V_(1F), V_(2F) to the DFE 612. The number of the outputs V_(i)to be used as tentative decisions depends on the required accuracy andspeed of decoding operation. After further delay, the output V₀ of thefirst MUX 1402 is also provided as the 4D tentative decision 44 (FIG. 2)to the Feedforward Equalizers 26 of the four constituent transceiversand the timing recovery block 222 (FIG. 2). The 4D symbol V_(9F), whichis the output V₉ of the 8:1 MUX 1420 delayed by one time unit, isprovided as the final decision 40 to the receive section of the PCS 204R(FIG. 2).

The following is the discussion on how outputs V₀ ^(i), V₁ ^(i), V_(0F),V_(1F), V_(2F) of the path memory module 608 might be used in the selectlogic 610, the MDFE 602, and the DFE 612 (FIG. 6).

FIG. 15 is a block level diagram of the ISI compensation portion of thedecoder, including construction and operational details of the DFE andMDFE circuitry (612 and 602 of FIG. 6, respectively). The ISIcompensation embodiment depicted in FIG. 15 is adapted to receive signalsamples from the deskew memory (36 of FIG. 2) and provide ISIcompensated signal samples to the Viterbi (slicer) for decoding. Theembodiment illustrated in FIG. 15 includes the Viterbi block 1502 (whichincludes the Viterbi decoder 604, the path metrics module 606 and thepath memory module 608), the select logic 610, the MDFE 602 and the DFE612.

The MDFE 602 computes an independent feedback signal for each of thepaths stored in the path memory module 608. These feedback signalsrepresent different hypotheses for the intersymbol interferencecomponent present in the input 37 (FIGS. 2 and 6) to the trellis decoder38. The different hypotheses for the intersymbol interference componentcorrespond to the different hypotheses about the previous symbols whichare represented by the different paths of the Viterbi decoder.

The Viterbi algorithm tests these hypotheses and identifies the mostlikely one. It is an essential aspect of the Viterbi algorithm topostpone this identifying decision until there is enough information tominimize the probability of error in the decision. In the meantime, allthe possibilities are kept open. Ideally, the MDFE block would use theentire path memory to compute the different feedback signals using theentire length of the path memory. In practice, this is not possiblebecause this would lead to unacceptable complexity. By “unacceptable”,it is meant requiring a very large number of components and an extremelycomplex interconnection pattern.

Therefore, in the exemplary embodiment, the part of the feedback signalcomputation that is performed on a per-path basis is limited to the twomost recent symbols stored in register set 0 and register set 1 of allpaths in the path memory module 608, namely V₀ ^(i) and V₁ ^(i) withi=0, . . . , 7, indicating the path. For symbols older than two periods,a hard decision is forced, and only one replica of a “tail” component ofthe intersymbol interference is computed. This results in some marginalloss of performance, but is more than adequately compensated for by asimpler system implementation.

The DFE 612 computes this “tail” component of the intersymbolinterference, based on the tentative decisions V_(0F), V_(1F), andV_(2F). The reason for using three different tentative decisions is thatthe reliability of the decisions increases with the increasing depthinto the path memory. For example, V_(1F) is a more reliable version ofV_(0F) delayed by one symbol period. In the absence of errors, V_(1F)would be always equal to a delayed version of V_(0F). In the presence oferrors, V_(1F) is different from V_(0F), and the probability of V_(1F)being in error is lower than the probability of V_(0F) being in error.Similarly, V_(2F) is a more reliable delayed version of V_(1F).

Referring to FIG. 15, the DFE 612 is a filter having 33 coefficients c₀through c₃₂ corresponding to 33 taps and a delay line 1504. The delayline is constructed of sequentially disposed summing junctions and delayelements, such as registers, as is well understood in the art of filterdesign. In the illustrated embodiment, the coefficients of the DFE 612are updated once every four symbol periods, i.e., 32 nanoseconds, inwell known fashion, using the well known Least Mean Squares algorithm,based on a decision input 1505 from the Viterbi block and an error input42dfe.

The symbols V_(0F), V_(1F), and V_(2F) are “jammed”, meaning inputted atvarious locations, into the delay line 1504 of the DFE 612. Based onthese symbols, the DFE 612 produces an intersymbol interference (ISI)replica portion associated with all previous symbols except the two mostrecent (since it was derived without using the first two taps of the DFE612). The ISI replica portion is subtracted from the output 37 of thedeskew memory block 36 to produce the signal 1508 which is then fed tothe MDFE block. The signal 1508 is denoted as the “tail” component inFIG. 6. In the illustrated embodiment, the DFE 612 has 33 taps, numberedfrom 0 through 32, and the tail component 1508 is associated with taps 2through 32. As shown in FIG. 15, due to a circuit layout reason, thetail component 1508 is obtained in two steps. First, the ISI replicaassociated with taps 3 through 32 is subtracted from the deskew memoryoutput 37 to produce an intermediate signal 1507. Then, the ISI replicaassociated with the tap 2 is subtracted from the intermediate signal1507 to produce the tail component 1508.

The DFE 612 also computes the ISI replica 1510 associated with the twomost recent symbols, based on tentative decisions V_(0F), V_(1F), andV_(2F). This ISI replica 1510 is subtracted from a delayed version ofthe output 37 of the deskew memory block 36 to provide a soft decision43. The tentative decision V_(0F) is subtracted from the soft decision43 in order to provide an error signal 42. Error signal 42 is furtherprocessed into several additional representations, identified as 42enc,42ph, and 42dfe. The error 42enc is provided to the echo cancelers andNEXT cancelers of the constituent transceivers. The error 42ph isprovided to the FFEs 26 (FIG. 2) of the four constituent transceiversand the timing recovery block 222. The error 42dfe is directed to theDFE 612, where it is used for the adaptive updating of the coefficientsof the DFE together with the last tentative decision V_(2F) from theViterbi block 1502. The tentative decision 44 shown in FIG. 6 is adelayed version of V_(0F). The soft decision 43 is outputted to a testinterface for display purposes.

The DFE 612 provides the tail component 1508 and the values of the two“initial” coefficients C₀ and C₁ to the MDFE 602. The MDFE 602 computeseight different replicas of the ISI associated with the first twocoefficients of the DFE 612. Each of these ISI replicas corresponds to adifferent path in the path memory module 608. This computation is partof the so-called “critical path” of the trellis decoder 38, in otherwords, the sequence of computations that must be completed in a singlesymbol period. At the speed of operation of the Gigabit Ethernettransceivers, the symbol period is 8 nanoseconds. All the challengingcomputations for 4D slicing, branch metrics, path extensions, selectionof best path, and update of path memory must be completed within onesymbol period. In addition, before these computations can even begin,the MDFE 602 must have completed the computation of the eight 4D Viterbiinputs 614 (FIG. 6) which involves computing the ISI replicas andsubtracting them from the output 37 of the de-skew memory block 36 (FIG.2). This bottleneck in the computations is very difficult to resolve.The system of the present invention allows the computations to becarried out smoothly in the allocated time.

Referring to FIG. 15, the MDFE 602 provides ISI compensation to receivedsignal samples, provided by the deskew memory (37 of FIG. 2) beforeproviding them, in turn, to the input of the Viterbi block 1502. ISIcompensation is performed by subtracting a multiplicity of derived ISIreplica components from a received signal sample so as to develop amultiplicity of signals that, together, represents various expressionsof ISI compensation that might be associated with any arbitrary symbol.One of the ISI compensated arbitrary symbolic representations is thenchosen, based on two tentative decisions made by the Viterbi block, asthe input signal sample to the Viterbi.

Since the symbols under consideration belong to a PAM-5 alphabet, theycan be expressed in one of only 5 possible values (−2, −1, 0, +1, +2).Representations of these five values are stored in a convolution engine1511, where they are convolved with the values of the first two filtercoefficients C₀ and C₁ of the DFE 612. Because there are two coefficientvalues and five level representations, the convolution engine 1511necessarily gives a twenty five value result that might be expressed as(a_(i)C₀+b_(j)C₁), with C₀ and C₁ representing the coefficients, andwith a_(i) and b_(j) representing the level expressions (with i=1, 2, 3,4, 5, and j=1, 2, 3, 4, 5 ranging independently).

These twenty five values are negatively combined with the tail component1508 received from the DFE 612. The tail component 1508 is a signalsample from which a partial ISI component associated with taps 2 through32 of the DFE 612 has been subtracted. In effect, the MDFE 602 isoperating on a partially ISI compensated (pre-compensated) signalsample. Each of the twenty five pre-computed values is subtracted fromthe partially compensated signal sample in a respective one of a stackof twenty five summing junctions. The MDFE then saturates the twentyfive results to make them fit in a predetermined range. This saturationprocess is done to reduce the number of bits of each of the 1Dcomponents of the Viterbi input 614 in order to facilitate lookup tablecomputations of branch metrics. The MDFE 602 then stores the resultantISI compensated signal samples in a stack of twenty five registers,which makes the samples available to a 25:1 MUX for input sampleselection. One of the contents of the twenty five registers willcorrespond to a component of a 4D Viterbi input with the ISI correctlycancelled, provided that there was no decision error (meaning the harddecision regarding the best path forced upon taps 2 through 32 of theDFE 612) in the computation of the tail component. In the absence ofnoise, this particular value will coincide with one of the ideal 5-levelsymbol values (i.e., −2, −1, 0, 1, 2). In practice, there will always benoise, so this value will be in general different than any of the idealsymbol values.

This ISI compensation scheme can be expanded to accommodate any numberof symbolic levels. If signal processing were performed on PAM-7signals, for example, the convolution engine 1511 would output fortynine values, i.e., a_(i) and b_(j) would range from 1 to 7. Error ratecould be reduced, i.e., performance could be improved, at the expense ofgreater system complexity, by increasing the number of DFE coefficientsinputted to the convolution engine 1511. The reason for this improvementis that the forced hard decision (regarding the best path forced upontaps 2 through 32 of the DFE 612) that goes into the “tail” computationis delayed. If C₂ were added to the process, and the symbols are againexpressed in a PAM-5 alphabet, the convolution engine 1511 would outputone hundred twenty five (125) values. Error rate is reduced bydecreasing the tail component computation, but at the expense of nowrequiring 125 summing junctions and registers, and a 125:1 MUX.

It is important to note that, as inputs to the DFE 612, the tentativedecisions V_(0F), V_(1F), V_(2F) are time sequences, and not justinstantaneous isolated symbols. If there is no error in the tentativedecision sequence V_(0F), then the time sequence V_(2F) will be the sameas the time sequence V_(1F) delayed by one time unit, and the same asthe time sequence V_(0F) delayed by two time units. However, due tooccasional decision error in the time sequence V_(0F), which may havebeen corrected by the more reliable time sequence V_(1F) or V_(2F), timesequences V_(1F) and V_(2F) may not exactly correspond to time-shiftedversions of time sequence V_(0F). For this reason, instead of using justone sequence V_(0F), all three sequences V_(0F), V_(1F) and V_(2F) areused as inputs to the DFE 612. Although this implementation isessentially equivalent to convolving V_(0F) with all the DFE'scoefficients when there is no decision error in V_(0F), it has the addedadvantage of reducing the probability of introducing a decision errorinto the DFE 612. It is noted that other tentative decision sequencesalong the depth of the path memory 608 may be used instead of thesequences V_(0F), V_(1F) and V_(2F).

Tentative decisions, developed by the Viterbi, are taken from selectedlocations in the path memory 608 and “jammed” into the DFE 612 atvarious locations along its computational path. In the illustratedembodiment (FIG. 15), the tentative decision sequence V_(0F) isconvolved with the DFE's coefficients C₀ through C₃, the sequence V_(1F)is convolved with the DFE's coefficients C₄ and C₅, and the sequenceV_(2F) is convolved with the DFE's coefficients C₆ through C₃₂. It isnoted that, since the partial ISI component that is subtracted from thedeskew memory output 37 to form the signal 1508 is essentially taken (intwo steps as described above) from tap 2 of the DFE 612, this partialISI component is associated with the DFE's coefficients C₂ through C₃₂.It is also noted that, in another embodiment, instead of using thetwo-step computation, this partial ISI component can be directly takenfrom the DFE 612 at point 1515 and subtracted from signal 37 to formsignal 1508.

It is noted that the sequences V_(0F), V_(1F), V_(2F) correspond to ahard decision regarding the choice of the best path among the eightpaths (path i is the path ending at state i). Thus, the partial ISIcomponent associated with the DFE's coefficients C₂ through C₃₂ is theresult of forcing a hard decision on the group of higher orderedcoefficients of the DFE 612. The underlying reason for computing onlyone partial ISI signal instead of eight complete ISI signals for theeight states (as done conventionally) is to save in computationalcomplexity and to avoid timing problems. In effect, the combination ofthe DFE and the MDFE of the present invention can be thought of asperforming the functions of a group of eight different conventional DFEshaving the same tap coefficients except for the first two tapcoefficients.

For each state, there remains to determine which path to use for theremaining two coefficients in a very short interval of time (about 16nanoseconds). This is done by the use of the convolution engine 1511 andthe MDFE 602. It is noted that the convolution engine 1511 can beimplemented as an integral part of the MDFE 602. It is also noted that,for each constituent transceiver, i.e., for each 1D component of theViterbi input 614 (the Viterbi input 614 is practically eight 4D Viterbiinputs), there is only one convolution engine 1511 for all the eightstates but there are eight replicas of the select logic 610 and eightreplicas of the MUX 1512.

The convolution engine 1511 computes all the possible values for the ISIassociated with the coefficients C₀ and C₁. There are only twenty fivepossible values, since this ISI is a convolution of these twocoefficients with a decision sequence of length 2, and each decision inthe sequence can only have five values (−2, −1, 0, +1, +2). Only one ofthese twenty five values is a correct value for this ISI. These twentyfive hypotheses of ISI are then provided to the MDFE 602.

In the MDFE 602, the twenty five possible values of ISI are subtractedfrom the partial ISI compensated signal 1508 using a set of addersconnected in parallel. The resulting signals are then saturated to fitin a predetermined range, using a set of saturators. The saturatedresults are then stored in a set of twenty five registers. Provided thatthere was no decision error regarding the best path (among the eightpaths) forced upon taps 2 through 32 of the DFE 612, one of the twentyfive registers would contain one 1D component of the Viterbi input 614with the ISI correctly cancelled for one of the eight states.

For each of the eight states, the generation of the Viterbi input islimited to selecting the correct value out of these 25 possible values.This is done, for each of the eight states, using a 25-to-1 multiplexer1512 whose select input is the output of the select logic 610. Theselect logic 610 receives V₀ ^((i)) and V₁ ^((i)) (i=0, . . . ,7) for aparticular state i from the path memory module 608 of the Viterbi block1502. The select logic 610 uses a pre-computed lookup table to determinethe value of the select signal 622A based on the values of V₀ ^((i)) andV₁ ^((i)) for the particular state i. The select signal 622A is onecomponent of the 8-component select signal 622 shown in FIG. 6. Based onthe select signal 622A, the 25-to-1 multiplexer 1512 selects one of thecontents of the twenty five registers as a 1D component of the Viterbiinput 614 for the corresponding state i.

FIG. 15 only shows the select logic and the 25-to-1 multiplexer for onestate and for one constituent transceiver. There are identical selectlogics and 25-to-1 multiplexers for the eight states and for eachconstituent transceiver. In other words, the computation of the 25values is done only once for all the eight states, but the 25:1 MUX andthe select logic are replicated eight times, one for each state. Theinput 614 to the Viterbi decoder 604 is, as a practical matter, eight 4DViterbi inputs.

In the case of the DFE, however, only a single DFE is contemplated forpractice of the invention. In contrast to alternative systems whereeight DFEs are required, one for each of the eight states imposed by thetrellis encoding scheme, a single DFE is sufficient since the decisionas to which path among the eight is the probable best was made in theViterbi block and forced to the DFE as a tentative decision. Statestatus is maintained at the Viterbi decoder input by controlling theMDFE output with the state specific signals developed by the 8 selectlogics (610 of FIG. 6) in response to the eight state specific signalsV₀ ^(i) and V₁ ^(i), i=0, . . . ,7, from the path memory module (608 ofFIG. 6). Although identified as a singular DFE, it will be understoodthat the 4D architectural requirements of the system means that the DFEis also 4D. Each of the four dimensions (twisted pairs) will exhibittheir own independent contributions to ISI and these should be dealtwith accordingly. Thus, the DFE is singular, with respect to statearchitecture, when its 4D nature is taken into account.

In the architecture of the system of the present invention, the Viterbiinput computation becomes a very small part of the critical path sincethe multiplexers have extremely low delay due largely to the placementof the 25 registers between the 25:1 multiplexer and the saturators. Ifa register is placed at the input to the MDFE 602, then the 25 registerswould not be needed. However, this would cause the Viterbi inputcomputation to be a larger part of the critical path due to the delayscaused by the adders and saturators. Thus, by using 25 registers at alocation proximate to the MDFE output instead of using one registerlocated at the input of the MDFE, the critical path of the MDFE and theViterbi decoder is broken up into 2 approximately balanced components.This architecture makes it possible to meet the very demanding timingrequirements of the Gigabit Ethernet transceiver.

Another advantageous factor in achieving high-speed operation for thetrellis decoder 38 is the use of heavily truncated representations forthe metrics of the Viterbi decoder. Although this may result in amathematically non-zero decrease in theoretical performance, theresulting vestigial precision is nevertheless quite sufficient tosupport healthy error margins. Moreover, the use of heavily truncatedrepresentations for the metrics of the Viterbi decoder greatly assistsin achieving the requisite high operational speeds in a gigabitenvironment. In addition, the reduced precision facilitates the use ofrandom logic or simple lookup tables to compute the squared errors,i.e., the distance metrics, consequently reducing the use of valuablesilicon real estate for merely ancillary circuitry.

FIG. 16 shows the word lengths used in one embodiment of the Viterbidecoder of this invention. In FIG. 16, the word lengths are denoted by Sor U followed by two numbers separated by a period. The first numberindicates the total number of bits in the word length. The second numberindicates the number of bits after the decimal point. The letter Sdenotes a signed number, while the letter U denotes an unsigned number.For example, each 1D component of the 4D Viterbi input is a signed 5-bitnumber having 3 bits after the decimal point.

FIG. 17 shows an exemplary lookup table that can be used to compute thesquared 1-dimensional errors. The logic function described by this tablecan be implemented using read-only-memory devices, random logiccircuitry or PLA circuitry. Logic design techniques well known to aperson of ordinary skill in the art can be used to implement the logicfunction described by the table of FIG. 17 in random logic.

FIGS. 18A and 18B provide a more complete table describing thecomputation of the decisions and squared errors for both the X and Ysubsets directly from one component of the 4D Viterbi input to the 1Dslicers (FIG. 7). This table completely specifies the operation of theslicers of FIG. 7.

An exemplary demodulator including a high speed decoder has beendescribed and includes various components that facilitate robust andaccurate acquisition and decoding of PAM-5 constellation signals atspeeds consistent with gigabit operation. Symbol decoding, including ISIcompensation, is accurately performed in a symbol period of about 8 ns,by a transceiver demodulator circuit constructed in a manner so as tofirst, bifurcate the ISI compensation function between an FFE, operatingto compensate partial response pulse shaping filter (remote transmitter)induced ISI, and a decoder operating to compensate ISI perturbationsinduced by transmission channel characteristics, and second, bybifurcating critical path computations into substantially balanced firstand second portions, the first portion including computations performedin a DFE and MDFE element and a second portion including computationsperformed in a Viterbi decoder.

The DFE element is further advantageous in that it is implemented asonly a single conceptual DFE (taking into account its 4D nature) ratherthan an eight element stack, each of which defines a multi-dimensionalinput to an eight-state Viterbi. The DFE is “stuffed”, at particularchosen locations, by the first several stages of a sequential,multi-stage tentative decision path memory module, so as to develop aset of “tail” coefficient values in the DFE which, taken together,represent the algebraic sum of a truncated set of DFE coefficients C₂ toC₃₂. A received symbol, represented by a five level constellation, isconvolved with the remaining two DFE coefficients, C₀ and C₁, which aretaken to represent the transmission channel induced ISI.

As deskewed signals enter the decoder, the previous symbol, convolvedwith the DFE coefficients C₃ to C₃₂, is first subtracted therefrom. Thenthe previous symbol convolved with C₂ is subtracted and the resultant(intermediate) symbol is directed to the MDFE. This resultant signalmight be described as the receive symbol with partial ISI introduced byprevious symbols subtracted. In the MDFE, all possible convolutions ofthe primary coefficients, C₀ and C₁, with the possible symbol values, issubtracted from the intermediate symbol to provide a receive symbolwithout perturbations induced by ISI.

It will be evident to one having skill in the art that although thetransceiver has been described in the context of a trellis encoded,PAM-5 signal representation, communicated over a multi-pair transmissionchannel, the invention is not limited to any particular communicationtechnique. Specifically, the decoder architecture and signal processingmethodology in accord with the invention is suitable for use with anyform of communication in which the symbolic content of the communicationis represented by multi-level signals. The invention, indeed, becomesparticularly appropriate as the number of signal levels increases.

Neither is the invention limited to signals encoded in accordance with a4D, eight-state, trellis methodology. Trellis encoding forces the systemto be constructed so as to accommodate the eight states inherent in thetrellis methodology. Other coding methodologies and architectures areexpressly contemplated by the invention and can be implemented by makingthe proper modifications to an alternative coding architecture's “statewidth”, as will be apparent to a skilled integrated circuit transceiverdesigner. Likewise, the “dimensional depth”, 1D, 2D, 4D . . . forexample, may be suitably increased, or decreased to accommodatedifferent forms of transmission channel implementations. As in the caseof increasing signal level representations, the systems and methods ofthe invention are particularly suitable for channels with increased“depth”, such as six, eight, or even higher numbers, of twisted paircabling, single conductor cabling, parallel wireless channels, and thelike.

While certain exemplary embodiments have been described in detail andshown in the accompanying drawings, it is to be understood that suchembodiments are merely illustrative of and not restrictive on the broadinvention. It will thus be recognized that various modifications may bemade to the illustrated and other embodiments of the invention describedabove, without departing from the broad inventive scope thereof. It willbe understood, therefore, that the invention is not limited to theparticular embodiments or arrangements disclosed, but is rather intendedto cover any changes, adaptations or modifications which are within thescope and spirit of the invention as defined by the appended claims.

What is claimed is:
 1. A symbol decoder included in a receiverconfigured to receive information encoded in accordance with amulti-level symbolic scheme and over a multi-dimensional transmissionchannel, the symbol decoder comprising: an input that is operative toreceive an input signal over the multi-dimensional transmission channel;a first slicer that is operative to process the input signal withrespect to a first one of two disjoint one-dimensional symbol-subsets; asecond slicer that is operative to process the input signal with respectto a second one of the two disjoint one-dimensional symbol-subsets; andwherein the first slicer outputs a first decision term and a first errorterm with respect to the first one of the two disjoint one-dimensionalsymbol-subsets, and the second slicer outputs a second decision term anda second error term with respect to the second one of the two disjointone-dimensional symbol-subsets.
 2. The symbol decoder according to claim1, wherein each of the first and second error terms represents adistance metric between the input signal and a symbol in the respectiveone of the two disjoint one-dimensional symbol-subsets.
 3. The symboldecoder according to claim 1, wherein each of the first and seconddecision terms represents a symbol in the respective one of the twodisjoint one-dimensional symbol-subsets.
 4. The symbol decoder accordingto claim 1, wherein each of the first and second error terms isexpressed by a digital representation having fewer than four bits. 5.The symbol decoder according to claim 1, wherein each of the first andsecond error terms is expressed by a digital representation having fewerthan three bits.
 6. The symbol decoder according to claim 1, wherein themulti-dimensional transmission channel has L dimensions and wherein thefirst and second error terms are 1-dimensional error terms, the1-dimensional error terms being combined to generate a set ofL-dimensional error terms such that each of the L-dimensional errorterms represents a distance between a received L-dimensional word and anearest codeword.
 7. A method for symbol decoding in a receiverconfigured to receive information encoded in accordance with amulti-level symbolic scheme and over a multi-dimensional transmissionchannel, the method comprising: receiving an input signal; processingthe input signal with respect to a first one of two disjointone-dimensional symbol-subsets in a first slicer to output a firstdecision term and a first error term with respect to the first one ofthe two disjoint one-dimensional symbol-subsets; and processing theinput signal with respect to a second one of the two disjointone-dimensional symbol-subsets in a second slicer to output a seconddecision term and a second error term with respect to the second one ofthe two disjoint one-dimensional symbol-subsets.
 8. The method accordingto claim 7, further comprising: producing from the first slicer a firstdecision with respect to the first one of the two disjointone-dimensional symbol-subsets; producing from the second slicer asecond decision with respect to the second one of the two disjointone-dimensional symbol-subsets; and producing a third decision from athird slicer with respect to the union set of the two disjointsymbol-subsets.
 9. The method according to claim 8, further comprising:combining the first decision with the third decision in a firstcombination block so as to define a first error term; and combining thesecond decision with the third decision in a second combination block soas to define a second error term.
 10. The method according to claim 9,further comprising: operating on the first error term so as to define asquare error representation thereof in a first square error block; andoperating on the second error term so as to define a square errorrepresentation thereof in a second square error block.
 11. The methodaccording to claim 10, wherein each of the first and second combinationblocks is implemented using a look-up table, the combination operationand error term definition being performed by consulting an appropriateentry in the look-up table.
 12. The method according to claim 10,wherein each of the first and second square error blocks is implementedusing a look-up table, the square error definition being performed byconsulting an appropriate entry in the look-up table.
 13. The methodaccording to claim 11, wherein the look-up table is implemented in aread-only memory storage device.
 14. The method according to claim 11,wherein the look-up table is implemented as a random logic integratedcircuit.
 15. The method according to claim 11, wherein the look-up tableis implemented as a programmable-logic-array integrated circuit.
 16. Themethod according to claim 10, wherein each of the first and second errorterms is expressed as a digital representation having one bit.